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How do you calculate the probability of rolling a total greater than 7 with two six-sided dice?

Ask by Mitchell Collins. in the United States
Feb 25,2025

Solución de inteligencia artificial de Upstudy

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The probability of rolling a total greater than 7 with two six-sided dice is 5/12.

Solución

When you roll two six-sided dice, there are a total of 6 × 6 = 36 possible outcomes. To calculate the probability of getting a sum greater than 7, follow these steps: 1. Identify the sums greater than 7: they are 8, 9, 10, 11, and 12. 2. Count the number of ways each of these sums can occur: • Sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 ways • Sum of 9: (3,6), (4,5), (5,4), (6,3) → 4 ways • Sum of 10: (4,6), (5,5), (6,4) → 3 ways • Sum of 11: (5,6), (6,5) → 2 ways • Sum of 12: (6,6) → 1 way 3. Add these up: 5 + 4 + 3 + 2 + 1 = 15 favorable outcomes. 4. Divide the number of favorable outcomes by the total number of outcomes: Probability = 15 / 36 = 5 / 12 (after simplifying by dividing by 3). So, the probability of rolling a total greater than 7 with two six-sided dice is 5/12.

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The Deep Dive

To find the probability of rolling a total greater than 7 with two six-sided dice, you first need to calculate the total possible outcomes, which is 6 x 6 = 36. Next, count the combinations that yield a sum greater than 7: (2,6), (3,5), (4,4), (4,5), (5,3), (5,2), (6,1), and so on. This gives you a total of 15 outcomes. Thus, the probability is 15/36 or 5/12. Now, if you're feeling a bit adventurous, why not simulate rolling the dice yourself? Grab a pair of six-sided dice and see how many times you can roll a total greater than 7! Track your results over, say, 50 rolls. It not only reinforces the probabilities but adds a sprinkle of real-life excitement to the challenge! Plus, you'll see firsthand how often those outcomes pan out!

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